I just opened a free Azure trial account and went through the various forms to create a test web app. I would like to edit the source files locally with Visual Studio 2015 howev
Web apps are accessible via ftp, so you can download/upload individual files.
However: The idea is that you should be editing locally, then pushing your changes to your web app deployment, not pulling from. To facilitate this, not only do you have ftp, but you also have git/github,bitbucket, dropbox, etc. just look under your Publishing settings, for Deployment Source: